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CORRECT BOHR MODEL
Lefteris Kaliambos (Natural Philosophy) March 31, 2015 The Bohr model of the hydrogen atom (Z = 1) or a hydrogen-like ion (Z > 1), where the negatively charged electron confined to an atomic shell encircles a small, positively charged atomic nucleus and where an electron jump between orbits is accompanied by an emitted or absorbed amount of electromagnetic energy (hν). The orbits in which the electron may travel are shown as grey circles; their radius increases as n2, where n is the principal quantum number. Note that according to my discovery of the "LAW OF ENERGY AND MASS" which rejects Einstein's invalid Mass-Energy Conservation. the electric energy ΔΕ of the electron-proton interaction in this figure turns to the energy hν of the photon in accordance with the conservation law of energy. Also according to the conservation law of mass the mass deffect Δm = ΔΕ/c2 turns to the mass m = hν/c2 of the same photon In atomic physics, the Bohr model introduced by Niels Bohr in 1913, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus - similar in structure to the solar system, but with attraction provided by electrostatic forces rather than gravity. After the Rutherford model (1911) came the Bohr model (1913). The improvement to the Rutherford model is mostly a quantum physical interpretation of it. The Bohr model has been superseded, but the quantum theory remains sound. But Bohr's Atomic Model is proved wrong according to the experiment conducted by Ernest Rutherford known as the "Rutherford's Gold Foil Experiment" The model's key success lay in explaining the Rydberg formula for the spectral emission lines of atomic hydrogen. While the Rydberg formula had been known experimentally, it did not gain a theoretical underpinning until the Bohr model was introduced. Not only did the Bohr model explain the reason for the structure of the Rydberg formula, it also provided a justification for its empirical results in terms of fundamental physical constants. The Bohr model is a relatively primitive model of the hydrogen atom, compared to the valence shell atom. As a theory, it can be derived as a first-order approximation of the hydrogen atom using the broader and much more accurate quantum mechanics and thus may be considered to be an obsolete scientific theory. However, because of its simplicity, and its correct results for selected systems, the Bohr model is still commonly taught to introduce students to quantum mechanics or energy level diagrams before moving on to the more accurate, but more complex, valence shell atom. The quantum theory of the period between Planck's discovery of the quantum (1900) and the advent of a full-blown quantum mechanics (1925) is often referred to as the old quantum theory. In the early 20th century, experiments by Ernest Rutherford established that atoms consisted of a diffuse cloud of negatively charged electrons surrounding a small, dense, positively charged nucleus. Given this experimental data, Rutherford naturally considered a planetary-model atom, the Rutherford model of 1911 – electrons orbiting a solar nucleus – however, said planetary-model atom has a technical difficulty. The laws of classical mechanics (i.e. the Larmor formula), predict that the electron will release electromagnetic radiation while orbiting a nucleus. Because the electron would lose energy, it would rapidly spiral inwards, collapsing into the nucleus on a timescale of around 16 picoseconds. This atom model is disastrous, because it predicts that all atoms are unstable. Also, as the electron spirals inward, the emission would rapidly increase in frequency as the orbit got smaller and faster. This would produce a continuous smear, in frequency, of electromagnetic radiation. However, late 19th century experiments with electric discharges have shown that atoms will only emit light (that is, electromagnetic radiation) at certain discrete frequencies. To overcome this difficulty, Niels Bohr proposed, in 1913, what is now called the Bohr model of the atom. He suggested that electrons could only have certain classical motions: Electrons in atoms orbit the nucleus. The electrons can only orbit stably, without radiating, in certain orbits (called by Bohr the "stationary orbits" at a certain discrete set of distances from the nucleus. These orbits are associated with definite energies and are also called energy shells or energy levels. In these orbits, the electron's acceleration does not result in radiation and energy loss as required by the Coulomb law. The Bohr model of an atom was based upon Planck's quantum theory of radiation. Electrons can only gain and lose energy by jumping from one allowed orbit to another, absorbing or emitting electromagnetic radiation with a frequency ν determined by the energy difference of the levels according to the Planck relation: ΔΕ = hν where h is Planck's constant. The significance of the Bohr model is that the laws of electromagnetism apply to the motion of the electron about the nucleus only when restricted by a quantum rule. Although a quantum rule is not completely well defined for small orbits, because the emission process involves two orbits with two different periods, Bohr could determine the energy spacing between levels using the quantum rule and come to an exactly correct quantum rule: the angular momentum L is restricted to be an integer multiple of a fixed unit: L = mυr = nħ where n = 1, 2, 3, ... is called the principal quantum number, and ħ = h/2π. The lowest value of n is 1; this gives a smallest possible orbital radius r = 0.0529 nm known as the Bohr radius. Here m is the mass of electron and υ is the velocity of it. Once an electron is in this lowest orbit,( ground state energy) it can get no closer to the proton. Starting from the angular momentum quantum rule, Bohr was able to calculate the energies of the allowed orbits of the hydrogen atom and other hydrogen-like atoms and ions, like Einstein's incomplete theory of the photoelectric effect,( see my CORRECT EXPLANATION OF PHOTOELECTRIC EFFECT). Under this condition Bohr in his paper “ On the Constitution of Atoms and Molecules” (1913) found that when an electron “falls from infinity” into the ground state energy it loses a total energy ΔΕ which is simply the sum of its kinetic energy mυ2/2 and its potential energy -Ke2/r of the Coulomb law. According to Newton’s second law and to the Coulomb law we can write mυ2/r = Ke2/r2 or mυ2/2 = 0.5Ke2/r So we get a total negative energy ΔΕ = mυ2/2 - Ke2/r = -0.5Ke2/r = hν Such an energy in terms of eV can be written as ΔΕ = -0.5Ke/r = 13.6 eV = hν However according to my discovery of the dipolic photon presented at the international conference "Frontiers of fundamental physics" (1993) the photon has not only energy E = hν but also mass m = hν/c2 .Note that Planck in 1907 in order to interpret the gravitational properties of light ( predicted by Newton and confirmed in 1801 by Soldner) showed that his quanta of light because of their energy do have mass. Also Einstein in 1938 in his famous book "The evolution of physics" (page 234) wrote: "A beam of light carries and energy has mass. But every inertial mass is attracted by the gravitational field, as inertial and gravitational masses are equivalent. A beam of light will bend in a gravitational field exactly as a body would if thrown horizontally with a velocity equal to that of light" Under this condition in the photoelectric effect the absorption of the particles of light by an electron contribute not only to the increase of the electron energy but also to the increase of the electron mass. See my Photon-matter interaction given by ΔΕ /ΔΜ = hν/m = c2 Therefore one sees that during the quantum jump also a mass defect ΔΜ = 13.6 eV/c2c2 turns into the photon mass m = hν/c2 It means that the simple Bohr model is an incomplete theory which should be modified by using not only the energy ΔΕ but also the mass defect ΔΜ = ΔΕ/c2 . It is of interest to note that the concept of mass defect ΔΜ of the later nuclear reactions at the time of Bohr (1913) was unknown. However It is indeed unfortunate that Einstein believed incorrectly that the mass defect ΔΜ turns into the photon energy hν. Such a fallacious idea did much to retard the progress of atomic and nuclear physics. Fortunately Bohr's condition, that the angular momentum is an integer multiple of ħ was later reinterpreted in 1924 by de Broglie as a standing wave condition: the electron is described by a wave and a whole number of wavelengths must fit along the circumference of the electron's orbit: In 1925 a new kind of mechanics was proposed, quantum mechanics, in which Bohr's model of electrons traveling in quantized orbits was extended into a more accurate model of electron motion. The new theory was proposed by Werner Heisenberg. Another form of the same theory, wave mechanics, was discovered by the Austrian physicist Erwin Schrödinger independently, and by different reasoning. Schrödinger employed de Broglie's matter waves, but sought wave solutions of a three-dimensional wave equation describing electrons that were constrained to move about the nucleus of a hydrogen-like atom, by being trapped by the potential of the positive nuclear charge. Category:Fundamental physics concepts